MathDB
n teams in a football tournament

Source: Ukraine TST 2015 p2

May 2, 2020
combinatorics

Problem Statement

In a football tournament, nn teams play one round (n2n \vdots 2). In each round should play n/2n / 2 pairs of teams that have not yet played. Schedule of each round takes place before its holding. For which smallest natural kk such that the following situation is possible: after kk tours, making a schedule of k+1k + 1 rounds already is not possible, i.e. these nn teams cannot be divided into n/2n / 2 pairs, in each of which there are teams that have not played in the previous kk rounds.
PS. The 3 vertical dots notation in the first row, I do not know what it means.